Evaluates the incomplete gamma function γ(a, x).

a—Integrand exponent parameter. It must be positive.

x—Upper limit of integration. It must be nonnegative.

result—The value of the incomplete gamma function γ(a, x).

Double—If present and nonzero, double precision is used.

The incomplete gamma function, γ(a, x), is defined as follows:

The incomplete gamma function is defined only for a > 0. Although γ(a, x) is well-defined for x > –infinity, this algorithm does not calculate γ(a, x) for negative x. For large a and sufficiently large x, γ(a, x) may overflow. Gamma function γ(a, x) is bounded by Γ(a), and users may find this bound a useful guide in determining legal values for a.

Plot the incomplete gamma function over [0.1, 1.1] × [0, 4]. The results are shown in Imcomplete Gamma Function Plot.

x = 4. * FINDGEN(25)/24

a = 1e-1 + FINDGEN(25)/24

b = FLTARR(25, 25)

FOR i=0L, 24 DO b(i, *) = GAMMAI(a(i), x)

!P.Charsize = 2.5

SURFACE, b, a, x, XTitle = 'a', YTitle = 'X'

MATH_NO_CONV_200_TS_TERMS—Function did not converge in 200 terms of Taylor series.

MATH_NO_CONV_200_CF_TERMS—Function did not converge in 200 terms of the continued fraction.